Optimal. Leaf size=13 \[ \frac {1}{4} \left (x^3+1\right )^{4/3} \]
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Rubi [A] time = 0.00, antiderivative size = 13, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {261} \begin {gather*} \frac {1}{4} \left (x^3+1\right )^{4/3} \end {gather*}
Antiderivative was successfully verified.
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Rule 261
Rubi steps
\begin {align*} \int x^2 \sqrt [3]{1+x^3} \, dx &=\frac {1}{4} \left (1+x^3\right )^{4/3}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 13, normalized size = 1.00 \begin {gather*} \frac {1}{4} \left (x^3+1\right )^{4/3} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [A] time = 0.01, size = 13, normalized size = 1.00 \begin {gather*} \frac {1}{4} \left (1+x^3\right )^{4/3} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.43, size = 9, normalized size = 0.69 \begin {gather*} \frac {1}{4} \, {\left (x^{3} + 1\right )}^{\frac {4}{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.44, size = 9, normalized size = 0.69 \begin {gather*} \frac {1}{4} \, {\left (x^{3} + 1\right )}^{\frac {4}{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.06, size = 10, normalized size = 0.77
method | result | size |
derivativedivides | \(\frac {\left (x^{3}+1\right )^{\frac {4}{3}}}{4}\) | \(10\) |
default | \(\frac {\left (x^{3}+1\right )^{\frac {4}{3}}}{4}\) | \(10\) |
risch | \(\frac {\left (x^{3}+1\right )^{\frac {4}{3}}}{4}\) | \(10\) |
trager | \(\left (\frac {x^{3}}{4}+\frac {1}{4}\right ) \left (x^{3}+1\right )^{\frac {1}{3}}\) | \(16\) |
meijerg | \(\frac {\hypergeom \left (\left [-\frac {1}{3}, 1\right ], \relax [2], -x^{3}\right ) x^{3}}{3}\) | \(17\) |
gosper | \(\frac {\left (1+x \right ) \left (x^{2}-x +1\right ) \left (x^{3}+1\right )^{\frac {1}{3}}}{4}\) | \(21\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.78, size = 9, normalized size = 0.69 \begin {gather*} \frac {1}{4} \, {\left (x^{3} + 1\right )}^{\frac {4}{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.13, size = 9, normalized size = 0.69 \begin {gather*} \frac {{\left (x^3+1\right )}^{4/3}}{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.16, size = 22, normalized size = 1.69 \begin {gather*} \frac {x^{3} \sqrt [3]{x^{3} + 1}}{4} + \frac {\sqrt [3]{x^{3} + 1}}{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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